Heat the oil in a medium skillet over medium-high heat, Add the onion and cook, stirring occasionally, until translucent, 2-3 minutes. Add the bell pepper, garlic, salt, black pepper and allspice, and cook, stirring, for 2 minutes more. Add the vinegar, molasses, Worcestershire, lime juice and tomato sauce, and cook for one minute more. Transfer the mixture to a blender or food processor, add the mango and jalapeños, and process until smooth.

Put two cups of the sauce into a large sealable (ziploc) bag with the chicken, and marinate for 1 hour in the refrigerator. Reserve the rest of the sauce for serving.

When you're ready to cook, heat a grill or stovetop grill pan to medium-high heat. Remove the chicken from the bag, discarding marinade. Grill the chicken just until cooked all the way through, approximately 4 minutes per side. Serve at room temperature, with the reserved sauce on the side. Or refrigerate and serve cold.